value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Definition of concavity, Definition 1: Given the function f (x ) then 1...

Definition 1: Given the function f (x ) then 1. f ( x ) is concave up in an interval I if all tangents to the curve on I are below the graph of f ( x ) . 2. f ( x ) is conca

Chi square distribution, Chi Square Distribution Chi square was first ...

Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d

Dimensions and degree of an expression, Binomials, Trinomials and P...

Binomials, Trinomials and Polynomials which we have seen above are not the only type. We can have them in a single variable say 'x' and of the form x 2 + 4

Uniform distribution over the interval, High temperatures in certain city i...

High temperatures in certain city in the month of August follow uniform distribution over the interval 60-85 F. What is probability that a randomly selected August day has a Temper

What is the connecticut sales tax on this item, Connecticut state sales tax...

Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10

Relationship between inverse and sine function, Relationship between the in...

Relationship between the inverse sine function and the sine function We have the given relationship among the inverse sine function and the sine function.

Example of inflection point - set theory and calculus, Need help, Determine...

Need help, Determine the points of inflection on the curve of the function y = x 3

Mechanics, find the composition of the simple harmonic motion of the same p...

find the composition of the simple harmonic motion of the same period in the perpendicular directions

Multiples, The sum of the smallest and largest multiples of 8 up to 60 is?

The sum of the smallest and largest multiples of 8 up to 60 is?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd